Question

Following transverse waves,
$y_{1}=2 \sin (100 \pi t-5.3 x) $,
$y_{2}=2 \sqrt{2} \sin \left(100-5.3 x+\frac{\pi}{4}\right)$
and $y_{3}=\sin (100 \pi t-5.3 x)$
superpose in a homogenous medium. Find the resultant amplitude at $x=0$.

• A. 1 unit
• B. 4 unit
• C. 5 unit
• D. 2 unit

Answer 1

Answer: (C)

Here,
$a_{x} =2+2 \sqrt{2} \cos \frac{\pi}{4} $
$=4 $ unit
$a_{y} =2 \sqrt{2} \sin 45^{\circ}+1 $
$=3$ unit
$A =\sqrt{A_{x}^{2}+a_{y}^{2}}$
$=\sqrt{4^{2}+3^{2}}=5 $ unit